1. Field of the Invention
The present invention relates to working method and apparatus of grinding a workpiece and particularly a non-circular workpiece such as a cam or the like, the workpiece being fixedly mounted on a workpiece head and ground by a cutting tool which engages the outer periphery of the workpiece while being rotated with the main spindle or shaft.
2. Description of the Related Art
An NC cylindrical grinding machine which is adapted to work non-circular workpieces by a combination of the rotation of a main spindle with the reciprocation of a grinding head having a grinding wheel requires data relating to the movement of the grinding head relative to the rotational angle of the main spindle. Such data will be referred to "X/C axes data". The X/C axes data is calculated from the shape data representing the non-circular configuration of the workpiece, the diameter of the grinding wheel and the revolution speed of the workpiece. The right half A of FIG. 1 shows a method of grinding a workpiece 12 while it is being rotated at a constant velocity, in accordance with the X/C axes data so calculated. The left half B of FIG. 1 shows another method of grinding a workpiece while changing the rotational velocity of the main spindle to make the circumferential velocity of the workpiece constant, in accordance with the X/C axes data. When the rotational velocity of the workpiece is constant (A), the rotational angle .theta..sub.1 of the rotating workpiece per given time period is also constant. On the other hand, when the circumferential velocity of the workpiece is constant (B), the distant of movement r.sub.1 of a contact point between the tool and the workpiece per given time period is constant.
FIG. 2 is a block diagram illustrating the electrical arrangement usable in the method of grinding the workpiece while the rotation of the main spindle is maintained constant. The arrangement comprises a servo system section 70 for controlling various shafts, a RAM 72 for storing a working program and variables relating to the controlled shafts, and a ROM 73 for storing software relating to the control of the shafts, the software being read upon power ON of the system. Various data are processed by a main processor 71. When a servo processor 74 receives commands of shaft movement from the main processor 71, the servo processor 74 mainly controls the acceleration and deceleration of the shafts and gives the commands of shaft movement to drive units 75. Each of the drive units 75 supplies an electric drive power to the servo motor of the corresponding shaft.
In order to calculate the X/C axes data from the data of non-circular configuration provided by a non-circle data pre-processing section 30 considering the diameter of the grinding wheel as well as the time required for the work to complete one revolution, a RAM 37 is provided which comprises a shape data storage section 31, a grinder diameter storage section 32, a main spindle revolution storage section 33 and an X/C axes data storage section 38. A processor 54 is also provided which comprises a cam profile calculating section 50 for converting a group of given angle and lift points into profile data, and an X/C axes data calculating section 55 for calculating the position of the grinding head and the angle of the main shaft.
FIG. 3 is a block diagram showing another electric arrangement for changing the rotational velocity of the main spindle to make the circumferential velocity of the workpiece constant. Such an arrangement is only different from the arrangement of FIG. 2 in that the processor 54 shown in FIG. 3 comprises a circumferential cam length calculating section 51 for calculating the circumferential length of the cam, and a profile dividing point calculating section 52 for dividing the determined profile into segments having equal length.
Since the revolution speed of the main spindle is constant when the rotational velocity of the workpiece is constant as described, there will not be any delay of control on changing the rotational velocity of the workpiece. Thus, such a method can completely prevent any error from be produced due to variations of the revolution speed of the main spindle. However, the velocity of movement of the contact point between the workpiece and the cutting tool becomes uneven, resulting in irregular grinding. This further results in an uneven reaction against the cutting tool. As shown by C in FIG. 1, for example, a transitional portion from the base circle to the raised part will have a rapid increase in the movement of contact point. Thus, the cutting resistance and associated reactive force on the tool are increased with an adverse affect on the life of the tool. Further, the grinding time is also insufficient to obtain the desired grinding, resulting in production of non-worked parts. When the cutting resistance increases, the workpiece itself becomes deformed which prevents contact between the workpiece and the cutting tool. This produces non-ground parts of the workpiece, leading to errors in working.
On the other hand, since the grinding is constantly carried out when the circumferential velocity of the workpiece is constant, the cutting resistance may be maintained constant. Thus, the above problems relating to the life of the tool and the non-worked parts can be overcome. However, this creates some delay on controlling the revolution speed of the main spindle to increase changes in velocity and acceleration. This may generate a chatter mark on the ground surface of the workpiece. The chatter mark is a wavy pattern resulting in degradation of the quality of product.
In both the related art methods described, the non-circular configuration is approximated to a group of line segments having minute lengths. In other words, the end points (division points) of each of the line segments are determined to specify the configuration of a workpiece. However, since the configuration of the workpiece is inherently curved, the number of division points becomes huge making the working control and calculation more complicated.